The Associative Property of Addition

Let's look at an example:
$2+10X+2X=2+12X$

We can group the second and third addends, add them, and then add the first addend to the result.
We will obtain an expression equivalent to the first expression since the associative property does not change the result.

Let's put a number in place of X to verify :

$X=3$
$2+10\times 3+2\times 3=2+12\times 3$

$2+30+6=2+36$
$38=38$

As we can see, after applying the associative property and adding the last two terms of the expression(the second and the third), and then adding the first term to the sum, the result is the same.
The associative property is an important and useful tool, so we recommend that you practice as much as possible until you can use it without thinking!

Task:

$7+8+12=$

Solution:

$7+8+12=15+12=27$

Answer:

$27$

Task:

$94+12+6=$

Solution:

$94+6+12=100+12=112$

Answer:

$112$

Task:

$13+37+45=$

$50+45=95$

Answer:

$95$

Task:

$4:2×\left(5+4+6\right)=$

Solution:

$2×\left(5+4+6\right)=$

$2\times(5+4+6)=$

$2\times(15)=$

$2\times(15)=30$

Answer:

$30$

Task:

$7\frac{2}{3}+6\frac{1}{6}+4\frac{1}{9}=\text{?}$

Solution:

$7\frac{2}{3}+6\frac{1}{6}+4\frac{1}{9}=$

$=7\frac{12}{18}+6\frac{3}{18}+4\frac{2}{18}=17+\frac{12+3+2}{18}$

$=7\frac{17}{18}=17\frac{17}{18}$

Answer:

$17\frac{17}{18}$

Task:

$6\times\frac{4}{5}x+7\times\frac{1}{2}x+4\times\frac{1}{3}x\times7.3x=\text{?}$

Solution:

$6\frac{4}{5}X+7\frac{1}{2}X+4\frac{1}{3}X\times7\frac{3}{10}X=\frac{34}{5}X+\frac{15}{2}X+\frac{13}{3}X\times\frac{73}{10}X$

$=\frac{68}{10}X+\frac{75}{10}X+\frac{13\times73}{3\times10}X²$

$=\frac{68+75}{10}X+\frac{949}{30}X²$

$=\frac{143}{10}X+31\frac{19}{30}X²=14.3X+31\frac{19}{30}X²$

Answer:

$14.3x+31\frac{19}{30}x²$

Task:

$4.1\times1.6\times3.2+4.7=\text{?}$

Solution:

$4.1\times1.6\times3.2+4.7=\text{?}$

$=4\frac{1}{10}\times1\frac{6}{10}\times3\frac{2}{10}+4\frac{7}{10}=$

$\frac{41}{10}\times\frac{16}{10}\times\frac{32}{10}+\frac{47}{10}=\frac{656}{100}\times\frac{32}{10}+\frac{47}{10}$

$\frac{41\times16}{10\times10}=\frac{656}{100}=\frac{656\times32}{100\times10}+\frac{47}{10}=$

$=\frac{20992}{1000}+\frac{4700}{1000}$

$=\frac{25692}{1000}=25.692$

Answer:

$25.692$

If you found this article helpful, you might also be interested in the following:

Commutative property of addition

The commutative property of multiplication

The associative property

Associative property of multiplication

The distributive property for students of 1st year of ESO

Distributive property

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